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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Differentiate the function.

g(x) = x2(1 – 2x)

To determine

To find: The differentiation of the function g(x).

Explanation

Given:

The function, g(x)=x2(12x).

Formula used:

The Constant Multiple Rule:

If c is a constant and f(x) is a differentiable function, then the constant multiple rule is,

ddx[cf(x)]=cddxf(x) (1)

The Power Rule:

If n is any real number, then the power rule is,

ddx(xn)=nxn1 (2)

The Difference Rule:

If f1(x) and f2(x) are both differentiable functions, then the difference rule is,

ddx[f1(x)f2(x)]=ddx(f1(x))ddx(f2(x)) (3)

Calculation:

The derivative of g(x)=x2(12x) is g(x), which is computed as follows

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